
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
The cards in a stack of $2n$ cards are numbered consecutively from 1 through $2n$ from top to bottom. Initially, the top $n$ cards are removed, kept in order, and form pile $A.$ The remaining cards form pile $B.$ The cards are then restacked by taking cards alternately from the tops of pile $B$ and pile $A.$ In this process, card number $(n+1)$ becomes the bottom card of the new stack. If, after the restacking process, card number 13 retains its original position, find the total number of cards in the stack.

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