
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
Binary numbers are defined as "carry over 2 to add 1", for example, (1101)<sub>2</sub> represents a binary number. Converting it into decimal form, it equals 1×2<sup>3</sup>+1×2<sup>2</sup>+0×2<sup>1</sup>+1×2<sup>0</sup>=13, which means (1101)<sub>2</sub> converted into a decimal number is 13. Similarly, we can define base-k numbers as "carry over k to add 1". Then, converting the base-3 number (102)<sub>3</sub> into a decimal number is $\boxed{11}$.

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