
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 that $\tan \alpha= \dfrac {1}{2}$, find the value of: $\dfrac {1+2\sin (\pi-\alpha)\cos (-2\pi-\alpha)}{\sin ^{2}(-\alpha)-\sin ^{2}( \dfrac {5\pi}{2}-\alpha)}$.

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