
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 the circle M: $(x-3)^2+(y-3)^2=4$, E and F are the midpoints of sides AB and BC of the inscribed equilateral triangle $\triangle ABC$ in the circle, respectively. When $\triangle ABC$ rotates around the center M of the circle, calculate the range of values for $\overrightarrow {ME}\cdot \overrightarrow {OF}$.

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