
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
For the four-digit number $\overline{a b c d}$, if $a > b$, $b < c$, and $c > d$, it is classified as a $P$ type number. If $a < b$, $b > c$, and $c < d$, it is classified as a $Q$ type number. What is the difference between the total number of $P$ type numbers and $Q$ type numbers?

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