
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
There are  $n$  cards numbered and stacked in increasing order from up to down (i.e. the card in the top is the number 1, the second is the 2, and so on...). With this deck, the next steps are followed:

-the first card (from the top) is put in the bottom of the deck.
-the second card (from the top) is taken away of the deck.
-the third card (from the top) is put in the bottom of the deck.
-the fourth card (from the top) is taken away of the deck.
- ...

The proccess goes on always the same way: the card in the top is put at the end of the deck and the next is taken away of the deck, until just one card is left. Determine which is that card.

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