
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 $\tan (π+α)=- \frac {1}{3}$ and $\tan (α+β)= \frac {\sin α+2\cos α}{5\cos α -\sin α }$.
(1) Find the value of $\tan (α+β)$;
(2) Find the value of $\tan β$.

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