
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 $α \in (0, \frac{π}{3})$ satisfies the equation $\sqrt{6} \sin α + \sqrt{2} \cos α = \sqrt{3}$, find the values of:
1. $\cos (α + \frac{π}{6})$
2. $\cos (2α + \frac{π}{12})$

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