
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
In the vertical equations, each letter represents a single digit; the same letter represents the same digit, and different letters represent different digits. The result of the operations specified in the column is shown below the line. Determine the value of each letter so that all six operations yield the correct result.

$$
\begin{array}{rlrl}
A B \cdot C A & =D E B \\
+\quad+ & = & : \\
F C-D G & = & D \\
\hline E G+H J & =A A G
\end{array}
$$



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