
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 2012 Hubei college entrance examination, a palindrome is defined as a positive integer that reads the same from left to right and from right to left, such as 22, 121, 3443, 94249, etc. It is evident that there are 9 two-digit palindromes: 11, 22, 33, ..., 99. There are 90 three-digit palindromes: 101, 111, 121, ..., 191, 202, ..., 999. Then,

(1) There are \_\_\_\_\_\_\_\_ four-digit palindromes;

(2) There are \_\_\_\_\_\_\_\_ palindromes with $2n + 1$ ($n \in \mathbb{N}^*$) digits.

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