
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
Given a regular octagon  $ABCDEFGH$  with side length  $3$ . By drawing the four diagonals  $AF$ ,  $BE$ ,  $CH$ , and  $DG$ , the octagon is divided into a square, four triangles, and four rectangles. Find the sum of the areas of the square and the four triangles.

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