
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
In square $ABCD$, two right-angled isosceles triangles are cut off from two opposite corners, $A$ and $C$, each with legs of length $x$. This leaves an irregular octagon. The combined area of the triangles cut off is $100 \text{ cm}^2$. Find the length of the shortest side of octagon, assuming $AB = 20$ cm.

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