
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 a triangular pyramid $S-ABC$, where $SA \perp$ plane $SBC$, $\angle BSC = 90^{\circ}$, $SC = 1$, and the dihedral angles $A-BC-S$ and $B-AC-S$ are $45^{\circ}$ and $60^{\circ}$, respectively. Find the surface area of the circumscribed sphere of the triangular pyramid $S-ABC$.

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