
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]


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Among all permutations of 1, 2, 3, 4, 5 in the form of $a_1a_2a_3a_4a_5$, find the total number of permutations that satisfy the conditions $a_1 < a_2$, $a_2 > a_3$, $a_3 < a_4$, and $a_4 > a_5$.

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