
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
Piravena needs to travel from city $X$ to city $Y$, from $Y$ to city $Z$, and then back to $X$. The cities form a right triangle with $Z$ a distance of 3600 km from $X$ and $Y$ a distance of 3900 km from $X$. The cost structure for travel includes:
- Bus: $\$0.20$ per kilometer.
- Airplane: $\$120$ booking fee plus $\$0.12$ per kilometer.

Calculate the least expensive total cost for Piravena to complete her journey.

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