
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 $m < 0$, and point M$(m, -2m)$ lies on the terminal side of angle $\alpha$, calculate the value of $$\frac {1}{2\sin\alpha \cos\alpha +\cos^{2}\alpha }$$.

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