
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 $\frac{{1+\tan\alpha}}{{1-\tan\alpha}}=2$, find the values of the following expressions:
1. $\frac{{\sin\alpha-2\cos\alpha}}{{2\sin\alpha-\cos\alpha}}$;
2. $\sin \alpha \cos \alpha +2$.

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