
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 square $PQRS$ with side $10$ feet. A circle is drawn with center $M$ such that it passes through vertices $P$ and $R$ and is tangent to side $PQ$ at point $T$. Find the radius of the circle.
A) $\sqrt{6}$ feet
B) $5\sqrt{6}$ feet
C) $5$ feet
D) $10\sqrt{2}$ feet
E) $10$ feet

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