
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 the diagram below, \(ABCD\) is a square. The points \(A, B\), and \(G\) are collinear. The line segments \(AC\) and \(DG\) intersect at \(E\), and the line segments \(DG\) and \(BC\) intersect at \(F\). Suppose that \(DE = 15 \text{ cm}\), \(EF = 9 \text{ cm}\), and \(FG = x \text{ cm}\). Find the value of \(x\).

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