
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 $f(x)=4\sin x\sin \left(x+ \frac {\pi}{3}\right)-1$.  
$(1)$ Calculate the value of $f\left( \frac {5\pi}{6}\right)$:  
$(2)$ Let $A$ be the smallest angle in $\triangle ABC$, and $f(A)= \frac {8}{5}$, find the value of $f\left(A+ \frac {\pi}{4}\right)$.

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