
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 terminal side of angle $\theta$ passes through the point $P({-\sqrt{3},\sqrt{6}})$.  
$(1)$ Find $\sin \theta$, $\cos \theta$, $\tan \theta$;  
$(2)$ Find $\sin 2\theta$, $\cos 2\theta$, $\tan 2\theta$.

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