
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
If the base $9$ representation of a perfect square is $bd4f_9$, with $b \ne 0$, find the possible value of $f$ among the digits from 0 to 8.
A) $\{0\}$  
B) $\{1\}$  
C) $\{4\}$  
D) $\{0, 1\}$  
E) $\{0, 1, 4\}$

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