
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
A cube with edge length 1 is denoted as AC<sub>1</sub>. A moving point P is on its surface, and the distance from point A is $\frac {2 \sqrt {3}}{3}$. The set of points P forms a curve. The length of this curve is \_\_\_\_\_\_.

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