
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 \(144 \, \text{cm}^2\), all its diagonals were marked. The hexagon thus "broke apart" into several triangles and quadrilaterals.

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

b) Determine the area of a regular hexagon formed by combining all the quadrilateral parts of the given hexagon.

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