
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
Let's consider a case where two lines in the plane are represented in vector form, and we want to determine if they are parallel:
\[\begin{pmatrix} 1 \\ 3 \end{pmatrix} + u \begin{pmatrix} 6 \\ -2 \end{pmatrix} = \begin{pmatrix} -4 \\ 5 \end{pmatrix} + v \begin{pmatrix} x \\ -3 \end{pmatrix}\]
Find the value of $x$ such that there are no solutions for $u$ and $v$, implying the lines do not intersect and are parallel.

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