
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 "stem-and-leaf" diagram is often used to represent whole numbers or decimal fractions. Suppose that in a studied group, there are 5 people aged 19, 34, 37, 42, and 48 years. The diagram would look like the one shown in the given problem. The left column is the "stem," and to the right are the "leaves."

In a certain group of patients, a doctor drew a stem-and-leaf diagram of their ages on December 1 (as shown in the first diagram). After several years, on another December 1, a new diagram of their ages was created with the same patients — no new patients joined the group, and all previous patients remained. Determine how many years have passed, and reconstruct the new diagram, where the digits are replaced by asterisks.

```
\begin{array}{l|llllll}
0 & & & & & & \\
1 & 0 & 0 & 1 & 2 & 2 & 3 \\
2 & 1 & 5 & 6 & & & \\
3 & 0 & 2 & 4 & 6 & & \\
4 & 1 & 6 & & & &
\end{array}
```

Given:
- Original Diagram (Fig. 3a)

Determine:
- Number of years elapsed.
- Reconstructed diagram (new ages) showing asterisks in place of the digits (Fig. 3b).

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