
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  $f_n(x)=\underbrace{xx\cdots x}_{n\ \text{times}}$  that is,  $f_n(x)$  is a  $n$  digit number with all digits  $x$ , where  $x\in \{1,2,\cdots,9\}$ . Then which of the following is  $\Big(f_n(3)\Big)^2+f_n(2)$ ?
[list=1]
[*]  $f_n(5)$ [*]  $f_{2n}(9)$ [*]  $f_{2n}(1)$ [*] None of these
[/list]

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