
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 line that passes through the points $\begin{pmatrix} -1 \\ 3 \end{pmatrix}$ and $\begin{pmatrix} 2 \\ 7 \end{pmatrix}$. This line has its direction vector in the form $\begin{pmatrix} 2 \\ b \end{pmatrix}$. Determine the value of $b$.

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