
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
A square \(ABCD\) has a side-length of 2, and \(M\) is the midpoint of \(BC\). The circle \(S\) inside the quadrilateral \(AMCD\) touches the three sides \(AM\), \(CD\), and \(DA\). What is its radius?

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