
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

	 Dodecagon  $QWARTZSPHINX$  has all side lengths equal to  $2$ , is not self-intersecting (in particular, the twelve vertices are all distinct), and moreover each interior angle is either  $90^{\circ}$  or  $270^{\circ}$ . What are all possible values of the area of  $\triangle SIX$ ?

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