
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
We are considering numbers that can be expressed as \(10 \times n + 1\), where \( \mathbf{n} \) is a positive integer. For example: \(11 = 10 \times 1 + 1\) and \(331 = 10 \times 33 + 1\). If such a number cannot be expressed as the product of two smaller numbers of the form \(10 \times n + 1\) (these two smaller numbers can be equal), we call this number a "Zhonghuan number". For example, \(341 = 11 \times 31\), since it can be expressed as the product of two numbers of the form \(10 \times n + 1\), it is not a "Zhonghuan number". However, 11 cannot be expressed as the product of two smaller numbers of the form \(10 \times n + 1\), so it is a "Zhonghuan number". How many "Zhonghuan numbers" are there among \(11, 21, 31, \ldots, 991\)?

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