
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
Given that $\triangle ABC$ is a right-angled triangle with $\angle ACB = 90^\circ$, and $AB = 10$. Point $P$ is a point outside the plane of $\triangle ABC$, and $PA = PB = PC$, with $PO \perp$ plane $ABC$, where $O$ is the foot of the perpendicular. Then, the length of $OC$ is $\boxed{5}$.

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