
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 points \( A(0,0) \), \( B(1,0) \), \( C(0,2) \), and \( D(3,3) \), point \( P \) is any point in the plane. Determine the minimum value of \( |PA| + |PB| + |PC| + |PD| \).

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