
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 \(A = \{a_1, a_2, \dots, a_{100}\}\) and \(B = \{b_1, b_2, \dots, b_{50}\}\), a mapping \(f\) from \(A\) to \(B\) is such that every element in \(B\) has a preimage, and
\[ f(a_1) \leq f(a_2) \leq \cdots \leq f(a_{100}) \]
Find the number of such mappings.

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