
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 $\triangle ABC$, $AC=6$, $BC=7$, $\cos A= \frac{1}{5}$, $O$ is the incenter of $\triangle ABC$, and $\overrightarrow{OP}=x \overrightarrow{OA}+y \overrightarrow{OB}$, where $0\leqslant x\leqslant 1$, $0\leqslant y\leqslant 1$. The area covered by the trajectory of point $P$ is $\_\_\_\_\_\_$.

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