
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 \( A=\{a_1, a_2, \cdots, a_{100}\} \) and \( B=\{b_1, b_2, \cdots, b_{50}\} \), if there is a mapping \( f \) from \( A \) to \( B \) such that each element in \( B \) has at least one preimage, and \( f(a_1) \leqslant f(a_2) \leqslant \cdots \leqslant f(a_{100}) \), determine the number of such mappings.

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