
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
Determine the real number \( m \) such that there is no solution for \( p \) and \( q \) in the equation:
\[
\begin{pmatrix} 4 \\ 7 \end{pmatrix} + p \begin{pmatrix} 5 \\ -9 \end{pmatrix}
=
\begin{pmatrix} 1 \\ -3 \end{pmatrix} + q \begin{pmatrix} -2 \\ m \end{pmatrix}
\]

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