
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
Given the digits $A$, $B$, $C$, and $D$, in the equations:
$$
\begin{array}{cc}
 & A\ B \\
+ & C\ D \\
\hline
 & A\ E \\
\end{array}
$$
and
$$
\begin{array}{cc}
 & A\ B \\
- & D\ C \\
\hline
 & A\ F \\
\end{array}
$$
Find the value of the digit $E$.

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