
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 that the terminal side of angle $\alpha$ passes through point $P(3a-9, a+2)$, and $\cos\alpha < 0$, $\sin\alpha > 0$, find the range of values for $a$;  
(2) Given that the terminal side of angle $\theta$ passes through point $P(-\sqrt{3}, \sqrt{6})$, find the value of $\cos(\theta - \frac{\pi}{6})$.

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