
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 \(0 \leq a, b, c, d \leq 1\). Find the possible values of the expression:
\[
\sqrt{(a^2)^2 + (b^2 - b^2)^2} + \sqrt{(b^2)^2 + (c^2 - b^2)^2} + \sqrt{(c^2)^2 + (d^2 - c^2)^2} + \sqrt{(d^2)^2 + (a^2 - d^2)^2}.
\]

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