
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
Given the quadratic function $y=-x^{2}+x+2$. When the values of the function $y$ corresponding to $a\leqslant x\leqslant a+3$ increase as $x$ increases, and the graph corresponding to it has a common point with the line $y=-4$, the range of values for $a$ is ______.

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