
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
Triangle \(ABC\) has \(AB = 5\), \(BC = 7\), and \(CA = 8\). New lines not containing but parallel to \(AB\), \(BC\), and \(CA\) are drawn tangent to the incircle of \(ABC\). What is the area of the hexagon formed by the sides of the original triangle and the newly drawn lines?

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