
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 points $P$, $A$, $B$, $C$ on the same sphere, $PA \perp$ plane $ABC$, $AP=2AB=2$, $AB=BC$, and $\overrightarrow{AB} \cdot \overrightarrow{BC} = 0$, find the surface area of the sphere.

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