
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
In the country of Wonderland, an election campaign is being held for the title of the best tea lover, with the candidates being the Mad Hatter, March Hare, and Dormouse. According to a poll, $20\%$ of the residents plan to vote for the Mad Hatter, $25\%$ for the March Hare, and $30\%$ for the Dormouse. The remaining residents are undecided. Determine the smallest percentage of the undecided voters that the Mad Hatter needs to secure to guarantee not losing to both the March Hare and the Dormouse (regardless of how the undecided votes are allocated), given that each undecided voter will vote for one of the candidates. The winner is determined by a simple majority. Justify your answer.

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