
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
An integer is called snakelike if its decimal representation $a_1a_2a_3\cdots a_k$ satisfies $a_i<a_{i+1}$ if $i$ is [ odd](https://artofproblemsolving.com/wiki/index.php/Odd_integer) and $a_i>a_{i+1}$ if $i$ is [ even](https://artofproblemsolving.com/wiki/index.php/Even_integer). How many snakelike integers between 1000 and 9999 have four distinct digits?

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