
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
Professor Antônio discovered an interesting property related to the integer $x$ that represents his age. He told his students that $x^{2}=\overline{a b a c}$ and that $x=\overline{a b}+\overline{a c}$. What is the professor's age?

Note: We are using a bar to distinguish the decimal representation of the four-digit number $\overline{a b c d}$ from the product $a \cdot b \cdot c \cdot d$. For example, if $\overline{a b c d}=1267$, then $a=1, b=2, c=6,$ and $d=7$. The notation is the same for numbers with other quantities of digits.

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