
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 $A=\{\sin\alpha, \cos\alpha, 1\}$, $B=\{\sin^2\alpha, \sin\alpha+\cos\alpha, 0\}$, and $A=B$, calculate the value of $\sin^{2009}\alpha+\cos^{2009}\alpha$.

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