
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. The top $n$ cards form pile $A$ while the remaining cards form pile $B$. When cards are restacked by alternating from piles $B$ and $A$, find the total number of cards in the stack where card number 161 retains its original position in a newly formed magical stack.

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