
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
Right triangle $PQR$ has a right angle at $P$ with leg $PQ = 9$ cm and leg $PR = 12$ cm. A square is positioned such that one side lies on hypotenuse $QR$ and one vertex of the square coincides with point $P$. Determine the length of one side of the square, expressed as a common fraction.

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