
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
Find the sum of all integers $k$ that can be expressed as a three-digit number in the base $-4+i$, where the digits are chosen from $\{0, 1, 2, \ldots, 16\}$. The expression for $k$ is\[ k = (a_2a_1a_0)_{-4+i} \]and $k$ is real.

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