
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
An equilateral triangle $PQR$ has a side length of $11$. There are three distinct triangles $PS_1T_1$, $PS_2T_2$, and $PS_3T_3$, each congruent to triangle $PQR$, with $QS_1 = QS_2 = QS_3 = 5$. Find $\sum_{k=1}^3 (RT_k)^2$.

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