
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
Pasha and Igor are flipping a coin. If it lands heads, Pasha wins; if tails, Igor wins. The first time the loser pays the winner 1 ruble, the second time 2 rubles, then 4 rubles, and so on (each time the loser pays twice as much as the previous step). After 12 games, Pasha became 2023 rubles richer than he was initially. How many of these games did he win?

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