
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
František Všímálek wrote consecutive numbers that are multiples of 3, 5, and 9. He did not write spaces between the numbers and proceeded as follows: first, he wrote the multiples of 3, then immediately after the last one, he started writing the multiples of 5, and finally, the multiples of 9. He noticed that symmetrical numbers appeared in his sequence (a symmetrical number reads the same backward as forward, e.g., 272, 3553, 98089). František wrote down all symmetrical numbers with three or more digits and arranged them in ascending order. Which number was in the third position in this sequence, and which one was the last?

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