
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
From $A=\{a_1, a_2, a_3, a_4\}$ to $B=\{b_1, b_2, b_3, b_4\}$, in the bijections, it is required that the image of $a_1$ cannot be $b_1$, and the preimage of $b_4$ cannot be $a_4$. There are $\boxed{14}$ such mappings.

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