
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
A natural two-digit number \( N \) was very envious of its friend, a two-digit decimal number \( X \), for its decimal point. So \( X \) gave it its decimal point. The number \( N \) inserted it between its two digits and didn't mind at all that it was now 567 tenths smaller than it was before. \( X \) was also satisfied because now it was twice as close to its friend \( N \) on the number line as it was before. Determine which two numbers \( N \) and \( X \) this story is about.

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