
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
(1) Given an angle $\alpha$ and a point $P(m,1)$ on its terminal side, with $\cos \alpha =-\dfrac{1}{3}$, find the value of $\tan \alpha$.

(2) Evaluate: $\dfrac{\tan 150^\circ \cos \left( -210^\circ \right)\sin \left( -420^\circ \right)}{\sin 1050^\circ \cos \left( -600^\circ \right)}$

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