
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 point $M(x_{1},y_{1})$ is on the graph of the function $y=-2x+8$. Find the range of values for $\frac{y_{1}+1}{x_{1}+1}$ when $x_{1}\in[2,5]$.

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