
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
Square  $ABCD$  has side length  $36$ .  Point  $E$  is on side  $AB$  a distance  $12$  from  $B$ , point  $F$  is the midpoint of side  $BC$ , and point  $G$  is on side  $CD$  a distance  $12$  from  $C$ .  Find the area of the region that lies inside triangle  $EFG$  and outside triangle  $AFD$ .

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