
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
Cities $A$, $B$, $C$, $D$, and $C'$ are connected by roads $\widetilde{AB}$, $\widetilde{AD}$, $\widetilde{AE}$, $\widetilde{BC}$, $\widetilde{BC'}$, $\widetilde{CD}$, and $\widetilde{DA}$. How many different routes are there from $A$ to $B$ that use each road exactly once, knowing that upon entering city $C$ or $C'$ you must immediately travel to city $D$?

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