
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
Petya, Vanya, Sergey, and Ivan Ivanovich are founders of a company with an initial capital. If Petya doubles his share of the initial capital, it will increase by $25\%$. If Vanya does the same, the capital will increase by $35\%$. If Sergey triples his share, the capital growth will be $40\%$. By how many times should Ivan Ivanovich increase his share of the capital so that his share exceeds $50\%$ of the initial capital?

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