
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
If the real and imaginary parts of a complex number correspond to the x-coordinate and y-coordinate of a vector, respectively, and it is known that $Z_1 = (1-2i)i$ corresponds to vector $\overrightarrow{a}$, and $Z_2 = \frac{1-3i}{1-i}$ corresponds to vector $\overrightarrow{b}$, then the dot product of $\overrightarrow{a}$ and $\overrightarrow{b}$ equals \_\_\_\_\_\_.

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