
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 an acute triangle $ABC$, where side $a$ is opposite angle $A$, side $b$ is opposite angle $B$, and side $c$ is opposite angle $C$, it is given that $(b^2 - a^2 - c^2) \sin A \cos A = ac \cos(A + C)$.
1. Find the measure of angle $A$.
2. If $a = \sqrt{2}$, find the maximum area of $\triangle ABC$.

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