
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 the vertex of angle $α$ is at the origin, and its initial side is the non-negative half-axis of the $x$-axis, if the terminal side of angle $α$ passes through point $P(x, -\sqrt{2})$, and $\cos α= \frac{\sqrt{3}}{6}x (x \neq 0)$, determine the quadrant in which angle $α$ is located, and find the values of $\sin α$ and $\tan α$.

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