
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 $\cos (α+ \frac {π}{6})- \sin α= \frac {3 \sqrt {3}}{5}$, find the value of $\sin (α+ \frac {5π}{6})$;
(2) Given $\sin α+ \sin β= \frac {1}{2}, \cos α+ \cos β= \frac { \sqrt {2}}{2}$, find the value of $\cos (α-β)$.

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