
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]


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Given that \( f(x) \) is a decreasing function defined on \( (0, +\infty) \). If \( f\left(2a^2 + a + 1\right) < f\left(3a^2 - 4a + 1\right) \) holds, then the range of values for \( a \) is ______.

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