
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 lemming starts at a corner of a square with a side length of 15 meters. It runs 9.3 meters along a diagonal toward the opposite corner, stops, makes a 90-degree right turn, and runs 3 more meters. Determine the average of the shortest distances from the lemming to each side of the square after it stops.

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