
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 the function \( f: \{a, b, c, d\} \rightarrow \{1, 2, 3\} \), if \( 10 < f(a) \cdot f(b) \) and \( f(c) \cdot f(d) < 20 \), calculate the number of possible mappings.

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