
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  $a,b, c$  denote the real numbers such that  $1 \le  a, b, c\le  2$ . 
Consider  $T = (a - b)^{2018} + (b - c)^{2018} + (c - a)^{2018}$ .
Determine the largest possible value of  $T$ .

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