
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 $a, b, c, d \geq 0$ such that $a + b + c + d = 1$. Find the maximum value of
\[
\sqrt[4]{abcd} + \sqrt[4]{(1-a)(1-b)(1-c)(1-d)}.
\]

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