
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 a regular hexagon with an area of \(144 \; \mathrm{cm}^{2}\), all its diagonals are marked. The hexagon is thus "divided" into several triangles and quadrilaterals.

a) Determine into how many parts the diagonals have divided it.

b) Determine the area of the regular hexagon that would be formed by the composition of all quadrilateral parts of the given hexagon.

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