
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
乙要猜甲的一个两位数, 如两个数字全对, 或一个对而另一个和正确数字相差为1, 甲说 “近”, 否则说 “远”. 例如, 甲的数是65, 如乙猜 $65,64,66,55$ 或75, 甲说 “近”, 否则说“远”.
(a) 求证: 乙不能仅猜18次,便保证能知道甲的数;
(b) 替乙找出一个仅猜24次的方法, 保证能知道甲的数;
(c) 有没有一个仅猜22次的方法?

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