
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
The study of some problems can go through the process of observation, conjecture, induction, and proof. The table below shows the research process of a problem.

| Steps |
|-------|
| **Observation:** 34+43=77 51+15=66 26+62=88 |
| **Conjecture:** The sum of two two-digit numbers obtained by interchanging the digits of the units and tens places is a two-digit number with the same digits in the units and tens places; the resulting two-digit number is divisible by 11... |
| **Verification:** 74+47=121, Is the original conjecture correct? ______. |
| **Further Verification:** Provide another example |
| **Proof:** Let a, b represent the digits on the tens and units places of a two-digit number, then |
| **Conclusion:** ______. |

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