
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 $0 \leq a \leq 1$, and let $b = 1$ and $c = 0$. Find the maximum value of:
\[
\sqrt{a\cdot 1 \cdot 0} + \sqrt{(1 - a)(1 - 1)(1 - 0)}.
\]

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