
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
When the digit $2$ is placed after a two-digit number whose tens' digit is $t$ and units' digit is $u$ in base-3 number system, the new number is:
A) $9t + u + 2$
B) $27t + 3u + 2$
C) $9t + 3u + 2$
D) $3t + u + 2$
E) $18t + 6u + 2$

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