
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
Let $O$ be the incenter of $\triangle ABC$, with $AB=5$, $AC=6$, and $BC=7$. If $OP = xOA + yOB + zOC$, where $0 \leq x, y, z \leq 1$, determine the area of the plane region covered by the locus of point $P$.

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