
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
In $\triangle PQR$, $PQ = 7$, $PR = 13$, $QR = 10$, and $S$ is the midpoint of $\overline{QR}$. What is the sum of the radii of the circles inscribed in $\triangle PQS$ and $\triangle PRS$?
A) $\sqrt{35}$
B) $\frac{20\sqrt{3}}{9+\sqrt{21}}$
C) $5\sqrt{2}$
D) $\frac{60}{11}$
E) $6\sqrt{3}$

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