
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 sits at a corner of a square with side length $15$ meters. It runs $9.3$ meters along a diagonal toward the opposite corner. It stops, makes a $45^{\circ}$ right turn and runs $3$ meters. Calculate the average of the shortest distances from the lemming to each side of the square.

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