
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
A cryptographer uses a modified encoding method for positive integers. First, the integer is written in base $5$. Then, he establishes a 1-to-1 correspondence between the digits in base $5$ and the elements of the set $\{A, B, C, D, E\}$. Using this correspondence, he finds that three consecutive integers in increasing order are coded as $ABE, ABD, AAC$, respectively. What is the base-$10$ expression for the integer coded as $BAC$?
A) 100
B) 105
C) 110
D) 115

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