
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
Evaluate $\sqrt{72 + 24\sqrt{6}}$ and express it in the form $a+b\sqrt{c}$, where $a$, $b$, and $c$ are integers, and $c$ has no factors which are the perfect square of any positive integer other than 1. Then find $a+b+c$.

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