
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 two sets of real numbers $A=\{a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\}$ and $B=\{b_{1}, b_{2}, b_{3}, b_{4}, b_{5}\}$, if there is exactly one element in $B$ without a pre-image and $f(a_{1}) \geq f(a_{2}) \geq f(a_{3}) \geq f(a_{4}) \geq f(a_{5})$, then there are \_\_\_\_\_\_ such mappings in total.

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