
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  $ABCD$ ,  $\overline{AC}$  and  $\overline{BD}$  meet at point  $E$ .
Point  $F$  is on  $\overline{CD}$  and  $\angle CAF = \angle FAD$ .
If  $\overline{AF}$  meets  $\overline{ED}$  at point  $G$ , and if  $\overline{EG} = 24$  cm, then find the length of  $\overline{CF}$ .

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