
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
Suppose that  $m$  and  $k$  are positive integers. Determine the number of sequences  $x_1, x_2, x_3, \dots , x_{m-1}, x_m$  with



- $x_i$  an integer for  $i = 1, 2, 3, \dots , m$ ,
- $1\le x_i \le k$  for  $i = 1, 2, 3, \dots , m$ ,
- $x_1\neq x_m$ , and
- no two consecutive terms equal.


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