
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
Given a positive integer $m$. Several honest people and $m$ ordinary people sit around a round table. Honest people never lie, while ordinary people might answer randomly. A person named A wants to find an honest person to make friends with. All people simultaneously tell A whether the next person in the clockwise direction is an honest person or an ordinary person. What is the maximum number of honest people such that A cannot guarantee finding a friend based solely on their responses?

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