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

(I) If $b=7$ and $a+c=13$, find the area of $\triangle ABC$.

(II) Find the maximum value of $\sqrt{3}\sin A + \sin(C - \frac{\pi}{6})$ and the size of angle $A$ when the maximum value is reached.

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