
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
In the coordinate plane, define points \( A = (0, 0) \), \( B = (8, 0) \), and \( C = (15, 0) \). Line \( \ell_A \) initially has a slope of 2 and passes through \( A \), Line \( \ell_B \) is vertical and passes through \( B \), and Line \( \ell_C \) initially has a slope of -2 and passes through \( C \). The three lines \( \ell_A \), \( \ell_B \), and \( \ell_C \) begin rotating clockwise about points \( A \), \( B \), and \( C \), respectively, at the rate of \( 10^\circ \) per second. At any given time, the three lines intersect to form a triangle. Determine the largest possible area of such a triangle.

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