
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
Each letter in the table represents a different digit, and different letters represent different digits. The leading digit of each number cannot be zero. The three numbers in each row from left to right form an arithmetic sequence, and the three numbers in each column from top to bottom also form an arithmetic sequence. What is the five-digit number $\overline{\mathrm{CDEFG}}$?

\begin{tabular}{|c|c|c|}
\hline
$A$ & $BA$ & $AA$ \\
\hline
$AB$ & $CA$ & $EF$ \\
\hline
$CD$ & $GA$ & $BDC$ \\
\hline
\end{tabular}

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