
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 \(a, b, c\) be real numbers such that \(a + b + c = 3,\) and \(a \ge -1,\) \(b \ge -2,\) and \(c \ge -3.\) Find the maximum value of
\[
\sqrt{2a + 2} + \sqrt{4b + 8} + \sqrt{6c + 18}.
\]

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