
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 it lands tails, Igor wins. Each time a player loses, they pay the winner 1 ruble the first time, 2 rubles the second time, 4 rubles the third time, and so on (each time the loser's payment doubles compared to the previous step). At the beginning of the game, Pasha had a single-digit amount of money, and Igor had a four-digit amount. By the end of the game, Igor had a two-digit amount, and Pasha had a three-digit amount. What is the minimum number of games that Pasha could have won? The players cannot go into debt.

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