
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 $f(x)=\sin (3x+ \frac {\pi}{3})+\cos (3x+ \frac {\pi}{6})+m\sin 3x$ ($m\in\mathbb{R}$), and $f( \frac {17\pi}{18})=-1$  
$(1)$ Find the value of $m$;  
$(2)$ In triangle $ABC$, with the sides opposite angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively, if $f( \frac {B}{3})= \sqrt {3}$, and $a^{2}=2c^{2}+b^{2}$, find $\tan A$．

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