
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
For each positive integer  $n$  let  $A_n$  be the  $n \times n$  matrix such that its  $a_{ij}$  entry is equal to  ${i+j-2 \choose j-1}$  for all  $1\leq i,j \leq n.$  Find the determinant of  $A_n$ .


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