
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 $\sin (α+ \frac {π}{3})+ \sin α= \frac {9 \sqrt {7}}{14}$, with $0 < α < \frac {π}{3}$:
(1) Find the value of $\sin α$;
(2) Find the value of $\cos (2α- \frac {π}{4})$.

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