
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 \(1 \leqslant a \leqslant 9\) and \(0 \leqslant b, c, d \leqslant 9\), if \(a > b, b < c, c > d\), then \(\overline{abcd}\) is called a \(P\)-type number. If \(a < b, b > c, c < d\), then \(\overline{abcd}\) is called a \(Q\)-type number. Let \(N(P)\) and \(N(Q)\) represent the number of \(P\)-type 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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