
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 $\overline{abcd}$ (where $1 \leq a \leq 9$ and $0 \leq b, c, d \leq 9$):
- If $a > b$, $b < c$, and $c > d$, then $\overline{abcd}$ is called a $P$-type number;
- If $a < b$, $b > c$, and $c < d$, then $\overline{abcd}$ is called a $Q$-type number.

Let $N(P)$ and $N(Q)$ denote the number of $P$-type numbers and $Q$-type numbers, respectively. Find the value of $N(P) - N(Q)$.

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