
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](https://artofproblemsolving.com/wiki/index.php/Integer) is called parity-monotonic if its decimal representation $a_{1}a_{2}a_{3}\cdots a_{k}$ satisfies $a_{i}<a_{i+1}$ if $a_{i}$ is [odd](https://artofproblemsolving.com/wiki/index.php/Odd), and $a_{i}>a_{i+1}$ if $a_{i}$ is [even](https://artofproblemsolving.com/wiki/index.php/Even). How many four-digit parity-monotonic integers are there?

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