The phrase "act substantially" is correct and usable in written English.
It can be used in contexts where you want to indicate that an action is significant or considerable in nature.
Example: "The committee decided to act substantially on the recommendations provided by the experts."
Alternatives: "take significant action" or "make considerable efforts".
In 1930, the United States passed the Smoot-Hawley Tariff Act, substantially raising U.S. import tariffs on foreign goods.
The Act substantially altered those relationships by superimposing pension obligations upon the company conspicuously beyond those that it had voluntarily agreed to undertake.
The Tydings McDuffie Act, substantially similar to the rejected measure but incorporating minor changes, was accepted by the Philippine Senate in 1934.
In overturning the Criminal Law Amendment Act of 1885 - the "blackmailer's charter" - the Sexual Offences Act substantially decriminalised homosexual acts and allowed gay men some freedom to live their lives openly and without fear.
In an opinion for the four dissenters, Justice David H. Souter objected that the majority had adopted an "exceedingly odd" and implausible interpretation that would leave the Voting Rights Act "substantially diminished".
Thus, we conclude that the observed basal N signal acts substantially through an endocytic route that requires cholesterol-dependent endocytosis and is thus distinguishable from ligand-induced signaling.
The ones who had gotten health insurance, mostly through the Affordable Care Act, were substantially less likely to report having trouble paying for medical care -- and substantially more likely to say their health care needs were being met.
While the NIRA was ruled unconstitutional, these policies persisted through the passage of the National Labor Relations Act, which substantially increased union bargaining power and led to further wage increases, including substantial increases just before the 1937-38 recession and through the continuation of lax antitrust enforcement.
The Affordable Care Act will substantially increase the number of Californians with health insurance.
On the 5th of March, 1867, a prior act, giving substantially the same powers to the village, was approved and became a law.
The Environmental Protection Agency said today that pending legislation to strengthen the Clean Air Act would substantially reduce the nation's dependence on foreign oil.
