
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
According to the table below, determine the range of values for a solution $x$ of the equation $ax^{2}+bx+c=0$ ($a\neq 0$, $a$, $b$, $c$ are constants).

|x|0.4|0.5|0.6|0.7|
|-|-|-|-|-|
|$ax^{2}+bx+c$|-0.64|-0.25|0.16|0.59|

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