
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

If \( 36 - 4 \sqrt{2} - 6 \sqrt{3} + 12 \sqrt{6} = (a \sqrt{2} + b \sqrt{3} + c)^{2} \), find the value of \( a^{2} + b^{2} + c^{2} \).
(a) 12  
(c) 14  
(b) 5  
(d) 6

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