
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  $a,b,c$  and  $m$  be integers such that  $0 \le m \le 26$ , and  $a + b + c = (a - b)(b- c)(c - a) \equiv m \pmod{27}$ . Determine the value of  $m$ .

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