
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 $0 \le a \le 1,$ $0 \le b \le 2,$ $0 \le c \le 1,$ and $0 \le d \le 1.$ Find the maximum value of 
\[
\sqrt[4]{abcd} + \sqrt{(1 - a)(1 - b)(1 - c)(1 - d)}.
\]

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