
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 teacher asked his students, Kolya and Seryozha, to each solve the same number of problems during the lesson. After some time, it turned out that Kolya had solved a third of what Seryozha still had left to solve, and Seryozha had half of his problems left to complete. Seryozha calculated that if he continued to solve the problems at the same rate, he would finish exactly by the end of the lesson. By what factor does Kolya need to increase his solving speed to finish all the problems by the end of the lesson?

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