
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 sets $A=\{x|x^2+x+a\leq0\}$, $B=\{x|x^2-x+2a-1<0\}$, $C=\{x|a\leq x\leq 4a-9\}$, and at least one of the sets $A$, $B$, $C$ is non-empty, then the range of values for $a$ is \_\_\_\_\_\_.

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