
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 $f(x)= \sqrt {3}\sin 2x+a\cdot \cos 2x$ ($a\in\mathbb{R}$).  
(I) If $f\left( \dfrac {\pi}{6}\right)=2$, find the value of $a$;  
(II) If $f(x)$ is monotonically decreasing on $\left[ \dfrac {\pi}{12}, \dfrac {7\pi}{12}\right]$, find the maximum value of $f(x)$.

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