
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
In $\triangle ABC$, it is known that $\overrightarrow {CD}=2 \overrightarrow {DB}$. $P$ is a point on line segment $AD$ and satisfies $\overrightarrow {CP}= \frac {1}{2} \overrightarrow {CA}+m \overrightarrow {CB}$. If the area of $\triangle ABC$ is $2 \sqrt {3}$, and $\angle ACB= \frac {\pi}{3}$, then the minimum value of $| \overrightarrow {CP}|$ is $\_\_\_\_\_\_$.

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