
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
The sum of the positive numbers \(a, b, c,\) and \(d\) does not exceed 4. Find the maximum value of the expression

$$
\sqrt[4]{2 a^{2}+a^{2} b} + \sqrt[4]{2 b^{2}+b^{2} c} + \sqrt[4]{2 c^{2}+c^{2} d} + \sqrt[4]{2 d^{2}+d^{2} a}
$$

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