
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 line passes through the distinct vectors $\mathbf{a}$ and $\mathbf{b}.$ For a certain value of $k$ and $m$, the vector
\[k \mathbf{a} + m \mathbf{b}\] must also lie on the line. Given that $m = \frac{5}{8}$, find $k$.

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