
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 $2n$. The top $n$ cards are moved to form pile $A$ and the remaining cards form pile $B$. Cards are then restacked alternately from piles $B$ and $A$. If card number $(n+1)$ becomes the bottom card of the new stack and card number 1 is just above it, continuing until both piles are exhausted. The stack is named magical if at least one card from each pile retains its original position. Determine the total number of cards in the magical stack where card number 161 retains its original position.

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