
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
On the ellipse $\frac {x^{2}}{2}+y^{2}=1$, for any three points M, A, B that are different from the vertices, there exists an acute angle $\theta$, such that $\overrightarrow {OM}=\cos\theta \overrightarrow {OA}+\sin\theta \overrightarrow {OB}$. Then, the product of the slopes of lines OA and OB is \_\_\_\_\_\_ .

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