
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 a pyramid \( M-ABCD \) with a square base, where \( MA = MD \) and \( MA \perp AB \), if the area of \( \triangle AMD \) is 1, find the radius of the largest sphere that can be inscribed in this pyramid.

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