
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 \(\triangle ABC\), \(AB : AC = 4 : 3\) and \(M\) is the midpoint of \(BC\). \(E\) is a point on \(AB\) and \(F\) is a point on \(AC\) such that \(AE : AF = 2 : 1\). It is also given that \(EF\) and \(AM\) intersect at \(G\) with \(GF = 72 \mathrm{~cm}\) and \(GE = x \mathrm{~cm}\). Find the value of \(x\).

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