
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
If the number of odd divisors of a number is \( 2^{m} \) (where \( m \) is a natural number), then we call such a number a "Zhonghuan number." For example, the number 3 has 2 odd divisors: 1 and 3, which is \( 2 = 2^1 \), so 3 is a "Zhonghuan number." Similarly, the number 21 has 4 odd divisors: 1, 3, 7, and 21, which is \( 4 = 2^2 \), so 21 is also a Zhonghuan number. We want to find the maximum value of \( n \) such that there are \( n \) consecutive Zhonghuan numbers. Find the maximum value of \( n \).

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