
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 $f(x)=A\sin (3x+ \frac {\pi}{6})+B(A > 0)$ has a maximum value of $2$ and a minimum value of $0$.  
$(1)$ Find the value of $f( \frac {7\pi}{18})$;  
$(2)$ After moving the graph of the function $y=f(x)$ to the right by $\frac {\pi}{6}$ units, and then expanding the ordinate of all points on the graph by $\sqrt {2}$ times while keeping the abscissa unchanged, we get the graph of the function $y=g(x)$. Find the solution of the equation $g(x)= \frac { \sqrt {2}}{2}$.

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