
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 $f(x)=2 \sqrt {3}\sin x\sin ( \frac {π}{2}-x)+2\cos ^{2}x+a$ with a maximum value of $3$.
(I) Find the interval where the function is monotonically increasing and the value of $a$;
(II) The graph of the function $y=f(x)$ is translated to the right by $\frac {π}{4}$ units to obtain the graph of the function $y=g(x)$. Find the range of $g(x)$ on $(0, \frac {π}{2})$.

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