
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 $A$, $B$, $C$ are denoted as $a$, $b$, and $c$, respectively. The function $f(x) = 2\cos{x}\sin(x - A)$ (where $x \in \mathbb{R}$) attains 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}
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