
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 fixed point \( A(a, 0) \) with \( a > 0 \) and the line \( l: x = -1 \). Point \( B \) is a variable point on the line \( l \). The angle bisector of \(\angle B(A\) intersects \( A B \) at point \( C \). Find the equation of the locus of point \( C \).

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