The phrase "along carefully" is correct and usable in written English.
It can be used to describe a manner of moving or proceeding with caution or attentiveness.
Example: "She walked along carefully, making sure not to trip on the uneven pavement."
Alternatives: "cautiously along" or "carefully along".
After a while, Mrs. Van Buren got up — stiffly and painfully, because of her arthritis — and accompanied me upstairs in a smart royal-blue elevator and then along carefully graded ramps for a look at her small but very pleasant apartment.
This movie moved us to tears because whatever battles raged between us, however ugly the other often appeared to be, we had these two very delicate fledglings that needed to be protected and carried along carefully, so carefully, because is anything more fragile than a preteenage girl or a growing, unsure boy?
This is somewhat frustrating: a walk-before-you-can-run approach is all well and good but, from the off, you can download vast amounts of courses that others have created, full of exotic elements like doors, Boos, lava and platforms that move along carefully delineated paths, but you can't properly edit those levels until you've played Super Mario Maker long enough to have acquired those elements.
Hausner guides the action along gently but confidently; there's rarely any doubt that she knows exactly what she's doing and that it's in our best interest to follow along carefully.
Doris, when she was along, watched carefully.
The listener followed Beethoven's thematic ideas along their carefully constructed paths.
Ms. Yates deployed walls of stucco and corrugated metal, along with carefully placed plantings, to achieve that.
The building's best features reside in the interior, along the carefully calibrated approach to the tomblike altar.
When Rosario left Mexico City to study in Cambridge, Mass., her mother sent along a carefully typewritten recipe for this relleno, which was traditionally for a Christmas turkey.
Kashmir is now divided along a carefully drawn line of control, but cross-border incursions — many of them bloody — occur daily.
Along with carefully selecting the plaintiffs, the lawyers working with Mr. Levy shaped their case in a second way, consciously keeping their distance from some groups that support gun rights.
