
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 that the angles $A$, $B$, and $C$ of $\triangle ABC$ form an arithmetic sequence, and the sides $a$, $b$, and $c$ form a geometric sequence.

1. Find the measure of angle $B$.
2. If the area of $\triangle ABC$ is $\sqrt{3}$, find the length of side $b$.

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