
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
If the vector $\vec{a} = (\sin\alpha, \cos\alpha - 2\sin\alpha)$ and the vector $\vec{b} = (1, 2)$ and $\vec{a}$ is parallel to $\vec{b}$, then find the value of $\dfrac{1+2\sin\alpha\cos\alpha}{\sin^{2}\alpha - \cos^{2}\alpha}$.

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