
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 $\triangle ABC$, sides $a$, $b$, and $c$ are opposite angles $A$, $B$, and $C$, respectively, and the angles $B$, $A$, and $C$ form an arithmetic sequence.
1. If $a^2 - c^2 = b^2 - mbc$, find the value of the real number $m$;
2. If $a = \sqrt{3}$, and $b + c = 3$, find the area of $\triangle ABC$.

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