
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 set $A$ and set $B$ both be the set of natural numbers $N$. The mapping $f: A \rightarrow B$ maps the element $n$ in set $A$ to the element $2^n + n$ in set $B$. Then, under the mapping $f$, the pre-image of $20$ is ____.

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