
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 rational numbers satisfying $(3a-2b+c-4)^2+(a+2b-3c+6)^2+(2a-b+2c-2)^2\leq 0$. Calculate $2a+b-4c$.

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