
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 that the side length of equilateral triangle ABC is 3, N is the midpoint of AB, and a point M on AB satisfies: $$\overrightarrow {CM}=x \overrightarrow {CA}+y \overrightarrow {CB}$$ (x > 0, y > 0), find the value of $$\overrightarrow {CM}\cdot \overrightarrow {AN}$$ when $$\frac {9}{x}+ \frac {1}{y}$$ is at its minimum.

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