
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 $f(x)=A\sin (2x+\varphi)$ ($A > 0$, $0 < \varphi < \pi$), $x\in\mathbb{R}$ has a maximum value of $1$, and its graph passes through the point $M\left( \frac {\pi}{6}, \frac { \sqrt {3}}{2}\right)$.  
(I) Find $\varphi$;  
(II) Find the intervals of monotonic increase for $f(x)$;  
(III) Through what kind of translation can the graph of $f(x)$ be modified so that the corresponding function becomes an odd function.

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