
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
How many integer triplets \((a, b, c)\) are there that satisfy the equation \(a+b+c=6\) along with the conditions \(-1 \leq a \leq 2\) and \(1 \leq b, c \leq 4\)?

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