
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
Let $0 \le a, b, c, d \le 2.$ Find the possible values of the expression
\[
\sqrt{a^2 + (2-b)^2} + \sqrt{b^2 + (2-c)^2} + \sqrt{c^2 + (2-d)^2} + \sqrt{d^2 + (2-a)^2}.
\]

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