
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 $m < 0$, a point $M(3m, -m)$ is on the terminal side of an angle $\alpha$. Then the value of $\frac{1}{2\sin\alpha\cos\alpha + \cos^2\alpha}$ is ( ).

A) $\frac{10}{7}$  
B) -2  
C) $\frac{2}{3}$  
D) $\frac{10}{3}$

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