
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
The circular window has nine panes of equal area. The inner circular pane has a radius of \(20 \mathrm{~cm}\) and the same centre, \(O\), as the outer circle. The eight lines separating the outer panes are of equal length, \(x \mathrm{~cm}\), and, if extended, would all pass through \(O\). Calculate the value of \(x\), to the nearest tenth.

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