
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 $\tan \left(\alpha+ \frac {\pi}{4}\right)= \frac {1}{3}$.

$(1)$ Find the value of $\tan \alpha$;  
$(2)$ Find the value of $2\sin ^{2}\alpha-\sin (\pi-\alpha)\sin \left( \frac {\pi}{2}-\alpha\right)+\sin ^{2}\left( \frac {3\pi}{2}+\alpha\right)$.

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