
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 following equations, each letter stands for a unique digit, with different letters representing different digits. The numbers underlined indicate the result of the operation in each column. Determine the values of the letters such that all the horizontal and vertical operations yield correct results.

\[
\begin{aligned}
\overline{a b} - \overline{c d} & = \overline{e d} \\
: \quad - & = - \\
e \cdot f & = \overline{d c} \\
\hline 
\overline{g d} + \overline{g b} & = \overline{h c}
\end{aligned}
\]

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