
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 $f(x)=2\sin x\cos x+2 \sqrt {3}\cos ^{2}x- \sqrt {3}$, where $x\in\mathbb{R}$.

(Ⅰ) Find the smallest positive period and the intervals of monotonic decrease for the function $y=f(-3x)+1$;

(Ⅱ) Given in $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If the acute angle $A$ satisfies $f\left( \frac {A}{2}- \frac {\pi}{6}\right)= \sqrt {3}$, and $a=7$, $\sin B+\sin C= \frac {13 \sqrt {3}}{14}$, find the area of $\triangle ABC$.

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