
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 a booklet with 65 pages numbered 1 to 65. Each page number is transformed as follows: if the original page number is $x$, then the new page number is found by reversing the order and increasing each resulting number by 3, i.e., $68 - x$. Determine how many pages have the same units digit in both the old page number and the transformed page number.

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