
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 $ABC$ with sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$ respectively, and $a$, $b$, $c$ form an arithmetic sequence with $C = 2A$,
1. Find $\cos A$.
2. If $a = \frac{4m^2 + 4m + 9}{m + 1}$ ($m > 0$), find the minimum value of the area of triangle $ABC$.

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