
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  $S$  be the set of all permutations of  $\{1, 2, 3, 4, 5\}$ . For  $s = (a_1, a_2,a_3,a_4,a_5) \in S$ , define  $\text{nimo}(s)$  to be the sum of all indices  $i \in \{1, 2, 3, 4\}$  for which  $a_i > a_{i+1}$ . For instance, if  $s=(2,3,1,5,4)$ , then  $\text{nimo}(s)=2+4=6$ . Compute \[\sum_{s\in S}2^{\text{nimo}(s)}.\]

*Proposed by Mehtaab Sawhney*

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