
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 that $α$ and $β$ are acute angles, and $\cos(α+β)= \frac {12}{13}$ and $\cos(2α+β)= \frac {3}{5}$, find the value of $\cos α$.
(2) Find the domain of the function $f(x)= \log_{10} (2\cos x-1)+ \sqrt {49-x^{2}}$.

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