
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
Consider a right triangle $ABC$ with $AB$ as the hypotenuse. A line moves through a fixed point $P$ inside the triangle, changing its slope steadily. The fixed point $P$ is located such that it divides the triangle into two regions, each having half the area of $ABC$. Determine the change in the angle $\theta$ between the moving line and base $BC$ as the line rotates from being parallel to side $AB$ to being parallel to side $AC$.

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