
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 two triangles $\triangle XYZ$ and $\triangle PQR$, where side $XY = 9$ cm, side $YZ = 21$ cm, and side $XZ = 15$ cm. Triangle $\triangle PQR$ has side $PQ = 3$ cm, side $QR = 7$ cm, and the angle $\angle PQR$ is the same as $\angle XYZ$. What is the length of segment $PR$?

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