
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
Let’s call a natural number a palindrome if its decimal representation reads the same from left to right and from right to left (the decimal representation cannot start with a zero; for example, the number 1221 is a palindrome, but the numbers 1231, 1212, and 1010 are not). Which type of palindromes among the numbers from 10,000 to 999,999 appear more frequently—those with an odd sum of digits or those with an even sum—and by what factor?

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