
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 sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. The function $f(x) = 2\cos x \sin (x - A) (x \in \mathbb{R})$ reaches its minimum value at $x = \frac{11\pi}{12}$.
1. Find the measure of angle $A$.
2. If $a = 7$ and $\sin B + \sin C = \frac{13\sqrt{3}}{14}$, find the area of $\triangle ABC$.

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