
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 new diagram, what is the perimeter of polygon $ABCDEF$? This hexagon is formed such that:
- $A=(0,7)$, $B=(4,7)$, $C=(4,4)$, $D=(7,0)$, $E=(0,0)$, and $F=(0,4)$.
- All coordinates reflect vertices connected in sequence from $A$ to $F$ with straight lines to form the hexagon.
- $AB=BC$, $CF$ extended meets $DE$ at $G$, and $AG$ is a straight line.

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