
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
There are many fascinating connections between mathematics and literature. In poetry, there are palindromic poems, such as: "云边月影沙边雁，水外天光山外树", which reads the same backward as forward: "树外山光天外水，雁边沙影月边云", offering a truly enjoyable experience in its imagery and rhyme! Similarly, in mathematics, there are palindromic numbers, such as: 88, 454, 7337, 43534, etc., which remain the same whether read from left to right or right to left, and are thus called "palindromic numbers", making them quite interesting to read!
There are 9 two-digit palindromic numbers: 11, 22, 33, 44, 55, 66, 77, 88, 99;
There are 90 three-digit palindromic numbers: 101, 111, 121, 131, …, 969, 979, 989, 999;
There are 90 four-digit palindromic numbers: 1001, 1111, 1221, …, 9669, 9779, 9889, 9999;
From this, infer the total number of ten-digit palindromic numbers.

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