
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 Land of Tria, numbers are represented in base \( r \). Olivia buys a house priced at \( 532_r \) monetary units (m.u.). She pays with a \( 1000_r \) m.u. bill and gets a two-step process in change: first \( 260_r \) m.u., second another \( 208_r \) m.u. Find the base \( r \) where these transactions make sense.
A) 5
B) 7
C) 8
D) 10
E) 12

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