
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
A permutation of a finite set  $S$  is a one-to-one function from  $S$  to  $S$ .  A permutation  $P$  of the set  $\{ 1, 2, 3, 4, 5 \}$  is called a W-permutation if  $P(1) > P(2) < P(3) > P(4) < P(5)$ .  A permutation of the set  $\{1, 2, 3, 4, 5 \}$  is selected at random.  Compute the probability that it is a W-permutation. 

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