
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 triangle \(T\),

a) Place the centrally symmetric polygon \(m\) with the largest possible area inside \(T\).

What is the area of \(m\) if the area of \(T\) is 1?

b) Enclose \(T\) in the centrally symmetric convex polygon \(M\) with the smallest possible area.

What is the area of \(M\) if the area of \(T\) is 1?

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