
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 $\triangle ABC$ is a right triangle with $\angle ACB=90^{\circ}$, $AB=8$, point $P$ is a point outside the plane of $ABC$. If $PA=PB=PC$, $PO\bot $ plane $ABC$, $O$ is the foot of the perpendicular, then $OC=\_\_\_\_\_\_$.

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