
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
Given the set \(A = \{x \mid 1 \leqslant x \leqslant 9, x \in \mathbf{Z}\}\) and the set \(B = \{(a, b) \mid a, b \in A\}\), define a mapping from \(B\) to \(\mathbf{Z}\) as \(f: (a, b) \rightarrow ab - a - b\), find the number of ordered pairs \((a, b)\) that satisfy \((a, b) \xrightarrow{f} 11\).

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