
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 that $\dfrac {3π}{4} < α < π$, and $\tan α+ \dfrac {1}{\tan α}=- \dfrac {10}{3}$.
(1) Find the value of $\tan α$;
(2) Find the value of $g(α)= \dfrac {\sin (π+α)+4\cos (2π-α)}{\sin ( \dfrac {π}{2}-α)-4\sin (-α)}$;
(3) If $β$, $γ$ are both acute angles, $\tan γ= \sqrt {3}(m-3\tan α)$, $\sqrt {3}(\tan γ\tan β+m)+\tan β=0$, find the value of $β+γ$.

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