
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
(1) Given $\cos (α+ \frac {π}{6})= \frac{1}{3}$, and $\frac {π}{6} < α < \frac {π}{2}$, find $\cos α$;
(2) Given $α$ and $β$ are both acute angles, and $\cos α= \frac{ \sqrt {5}}{5}$, $\cos β= \frac{ \sqrt {10}}{10}$, find $α+β$.

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