
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
The letters $E$, $F$, $G$, and $H$ represent digits. Consider the equations represented by the additions and subtractions below: 
$$
\begin{tabular}{ccc}
&E&F\\ 
+&G&E\\ 
\hline 
&H&E
\end{tabular}
$$
and
$$
\begin{tabular}{ccc}
&E&F\\ 
-&G&E\\ 
\hline 
&&E
\end{tabular}
$$
What is the value of the digit $H$?

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