
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given a right triangle $ABC$ with $\angle BAC = 90^\circ$, a line segment moves parallel to the hypotenuse $BC$ from vertex $A$ towards the opposite side $BC$. When the segment starts moving, it has a length of zero, and when it reaches $BC$, it again has a length of zero. At its maximum length, the line segment is aligned with the altitude from vertex $A$ to side $BC$. If side $AB$ is 3 units and side $AC$ is 4 units, find the maximum length of the moving line segment.
A) 2.4 units
B) 3.0 units
C) $\frac{15}{4}$ units
D) $\frac{12}{5}$ units

Present the answer in LaTex format: \boxed{Your answer}
user