
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 $f(x)=2\cos x\cdot\sin \left(x+ \dfrac {\pi}{3}\right)- \sqrt {3}\sin ^{2}x+\sin x\cdot\cos x$.  
$(1)$ Find the interval of monotonic decrease for the function $f(x)$;  
$(2)$ After translating the graph of function $f(x)$ by the vector $ \overrightarrow{a}=(m,0)$, we obtain the graph of $g(x)$. Find the smallest positive value of $m$ that makes $g(x)$ an even function.

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