
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  $n\ge2$  be a positive integer. Given a sequence  $\left(s_i\right)$  of  $n$  distinct real numbers, define the "class" of the sequence to be the sequence  $\left(a_1,a_2,\ldots,a_{n-1}\right)$ , where  $a_i$  is  $1$  if  $s_{i+1} > s_i$  and  $-1$  otherwise.

Find the smallest integer  $m$  such that there exists a sequence  $\left(w_i\right)$  of length  $m$  such that for every possible class of a sequence of length  $n$ , there is a subsequence of  $\left(w_i\right)$  that has that class.

*David Yang.*

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