
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
Consider numbers of the form  $1a1$ , where  $a$  is a digit. How many pairs of such numbers are there such that their sum is also a palindrome?

*Note: A palindrome is a number which reads the same from left to right and from right to left. Examples:  $353$ ,  $91719$ .*

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