
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 $x,$ $y,$ $z$ be real numbers such that $x + y + z = 3,$ and $x \ge -1,$ $y \ge -2,$ and $z \ge -3.$ Find the maximum value of
\[
\sqrt{4x + 4} + \sqrt{4y + 8} + \sqrt{4z + 12}.
\]

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