
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 Berk tries to guess the two-digit number that Ayca picks, after each guess, Ayca gives a hint indicating the number of digits which match the number picked. If Berk can guarantee to guess Ayca's number in  $n$  guesses, what is the smallest possible value of  $n$?

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