
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
Let the set $$M=\{x|x=\sin \frac {n\pi}{3}, n\in\mathbb{Z}\}$$. Determine the number of sets $P$ that satisfy the condition $$P\cup\left\{ \frac { \sqrt {3}}{2}, - \frac { \sqrt {3}}{2}\right\}=M$$

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