
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 are removed, forming pile $A$, and the remaining cards form pile $B$. The cards are restacked by alternatively taking cards from the tops of piles $B$ and $A$. Assume card number $(n+1)$ becomes the bottom card of the new stack. Determine $n$ if card number 149 must retain its original position in the stack.

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