The phrase "assess exactly" is correct and usable in written English.
It can be used when you want to emphasize the precision or specificity of an evaluation or judgment.
Example: "In order to improve our project outcomes, we need to assess exactly how each team member contributes to the overall success."
Alternatives: "evaluate precisely" or "analyze accurately".
Weather experts were still trying to assess exactly what had produced such damage.
Confusion reigned on Monday as relatives and lawyers tried to assess exactly where the women were sent.
And, in general, it is difficult to assess exactly how Apple's ethical and environmental record compares to other companies.
The defense force plans to send three helicopters flying over the Limpopo River valley on Saturday to assess exactly how many people are still waiting to be rescued.
Before 2009, Solazyme also shared technical details of their "platform," making it a little easier to assess exactly how they were tinkering with life.
"But the campaign being waged against the BNP is also more sophisticated and targeted than before so it is difficult to assess exactly what will happen".
For our pre-civilised ancestors, the exposed breasts of a woman would have been a quick and easy way of assessing exactly where she was in her life.
But assessing exactly how bad it is — how angry or loyal people feel, how effective or cruel the closure has been, how truly impoverished Gaza has become — is a delicate and politically fraught activity as three recent days of reporting here and dozens of interviews showed.
"Big data, cloud providers, global multinationals, large Internet and tech companies — I think all are spending a lot of time today assessing exactly what their risks are and what this means," he adds.
Although the moderately strong correlation coefficients did indicate some degree of overlap between the skills and abilities being assessed by the three tasks, the correlations were not strong enough to suggest that they were assessing exactly the same things.
"We're still assessing exactly how narrow it is and determining what kind of impact it actually would have," Earnest said in his daily briefing.
