
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 triangle \(ABC\), \(AB = 13\), \(BC = 14\), \(CA = 15\). Squares \(ABB_1A_2\), \(BCC_1B_2\), \(CAA_1C_2\) are constructed outside the triangle. Squares \(A_1A_2A_3A_4\), \(B_1B_2B_3B_4\), \(C_1C_2C_3C_4\) are constructed outside the hexagon \(A_1A_2B_1B_2C_1C_2\). Squares \(A_3B_4B_5A_6\), \(B_3C_4C_5B_6\), \(C_3A_4A_5C_6\) are constructed outside the hexagon \(A_4A_3B_4B_3C_4C_3\). Find the area of the hexagon \(A_5A_6B_5B_6C_5C_6\).

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