
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
Triangle $PQR$ has vertices $P(1, 9)$, $Q(3, 2)$, and $R(9, 2)$. A line through $Q$ cuts the area of $\triangle PQR$ in half and has a $y$-intercept of $1$. Find the slope of this line and then find the sum of the slope and $y$-intercept.

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