
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 the vectors $\overrightarrow{OA} = (1, -7, 8)$, $\overrightarrow{OB} = (0, 14, 16)$, and $\overrightarrow{c} = (\sqrt{2}, \frac{1}{7}\sin\alpha, \frac{1}{8}\cos\alpha)$, where $\alpha$ is in the interval $(0, \pi)$, if $\overrightarrow{c}$ is perpendicular to plane OAB, then find the value of $\alpha$.

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