
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 the function $f(x) = 2\sin x\cos x + 2\sqrt{3}\cos^2x - \sqrt{3}$,  
(1) Find the smallest positive period and the intervals of monotonic decrease for the function $y = f(-2x) + 1$;  
(2) Given in $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If acute angle $A$ satisfies $f\left(\frac{A}{2} - \frac{\pi}{6}\right) = \sqrt{3}$, and $a=8$, $\sin B + \sin C = \frac{13\sqrt{3}}{16}$, find the area of $\triangle ABC$.

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