
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
In the xy-plane with a rectangular coordinate system, let vector $\overrightarrow {a}$ = (cosα, sinα) and vector $\overrightarrow {b}$ = (sin(α + π/6), cos(α + π/6)), where 0 < α < π/2.
(1) If $\overrightarrow {a}$ is parallel to $\overrightarrow {b}$, find the value of α.
(2) If tan2α = -1/7, find the value of the dot product $\overrightarrow {a}$ • $\overrightarrow {b}$.

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