
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 museum hall contained a square sheet of iron (with a side length of 3.414 meters); such iron was once used to make knight armor. The museum keeper decided that this exhibit would look more interesting (possibly even somewhat reminiscent of an ancient knight's shield) if the four corners of this sheet were cut into four triangular notches, so that instead of a square, an octagon with equal sides would be visible. The craftsman tasked with this job wondered what the dimensions of the triangular notches should be. Help him.

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