
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 the three-dimensional Cartesian coordinate system, it is known that point $P(1, 2, 3)$. The symmetric point of $P$ with respect to the plane $xOy$ is $P_0$. Then, the distance $|PP_0|$ equals \_\_\_\_\_\_\_\_.

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