
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 $DEF$ has one leg of length 7 cm, another leg of length 24 cm, and a right angle at $D$. A square has one side on the hypotenuse of triangle $DEF$ and a vertex on each of the two legs of triangle $DEF$. What is the length of one side of the square, in cm? Express your answer as a common fraction.

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