
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
There are 22 black and 3 blue balls in a bag. Ahmet chooses an integer  $ n$  in between 1 and 25. Betül draws  $ n$  balls from the bag one by one such that no ball is put back to the bag after it is drawn. If exactly 2 of the  $ n$  balls are blue and the second blue ball is drawn at  $ n^{th}$  order, Ahmet wins, otherwise Betül wins. Calculate the value of  n  that maximizes the chance for Ahmet to win.

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