
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
Given real numbers \(a, b, c \geqslant 1\) that satisfy the equation \(a b c + 2 a^{2} + 2 b^{2} + 2 c^{2} + c a - c b - 4 a + 4 b - c = 28\), find the maximum value of \(a + b + c\).

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