
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 $\triangle ABC$, $AB=5$, $AC=6$, $\cos A=\frac{1}{5}$, $O$ is the circumcenter of $\triangle ABC$. If $\overrightarrow{OP}=x\overrightarrow{OB}+y\overrightarrow{OC}$, where $x$, $y\in \left[0,1\right]$, then the area covered by the trajectory of point $P$ is ______.

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