
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
The volume of the parallelepiped generated by $\begin{pmatrix} 3 \\ 4 \\ 5 \end{pmatrix},$ $\begin{pmatrix} 2 \\ k \\ 3 \end{pmatrix},$ and $\begin{pmatrix} 2 \\ 3 \\ k \end{pmatrix}$ is 20. Find $k,$ where $k > 0.$

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