
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 $$α∈(0， \frac {π}{3})$$ and vectors $$a=( \sqrt {6}sinα， \sqrt {2})$$, $$b=(1，cosα- \frac { \sqrt {6}}{2})$$ are orthogonal,

(1) Find the value of $$tan(α+ \frac {π}{6})$$;

(2) Find the value of $$cos(2α+ \frac {7π}{12})$$.

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