
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 $0 \leq p, q, r, s \leq 1$. Find the possible values of the expression
\[
\sqrt{p^2 + (1 - q)^2} + \sqrt{q^2 + (1 - r)^2} + \sqrt{r^2 + (1 - s)^2} + \sqrt{s^2 + (1 - p)^2}.
\]

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