
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 a point P(m, 3m) on the terminal side of angle $\alpha$ (m ≠ 0), find the value of $\cos^2\alpha-3\sin\alpha\cos\alpha$;  
(2) Given $\sin\theta= \frac{1-a}{1+a}$ and $\cos\theta= \frac{3a-1}{1+a}$, if $\theta$ is an angle in the second quadrant, find the value of the real number $a$.

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