
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 that $A$ is an interior angle of $\triangle ABC$, when $x= \frac {5\pi}{12}$, the function $f(x)=2\cos x\sin (x-A)+\sin A$ attains its maximum value. The sides opposite to the angles $A$, $B$, $C$ of $\triangle ABC$ are $a$, $b$, $c$ respectively.  
$(1)$ Find the 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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