
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  $A$  and  $B$  be points on a circle  $\mathcal{C}$  with center  $O$  such that  $\angle AOB = \dfrac {\pi}2$ . Circles  $\mathcal{C}_1$  and  $\mathcal{C}_2$  are internally tangent to  $\mathcal{C}$  at  $A$  and  $B$  respectively and are also externally tangent to one another. The circle  $\mathcal{C}_3$  lies in the interior of  $\angle AOB$  and it is tangent  externally to  $\mathcal{C}_1$ ,  $\mathcal{C}_2$  at  $P$  and  $R$  and internally tangent to  $\mathcal{C}$  at  $S$ . Evaluate the value of   $\angle PSR$ .

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