
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
Let \( A = \{a_1, a_2, a_3\} \), \( B = \{b_1, b_2, b_3, b_4\} \). Then the number of one-to-one mappings from \( A \) to the subsets of \( B \) is _____. The number of mappings from \( A \) to the subsets of \( B \) is _____.

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