
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 function $f(x)=\begin{cases} -x^2 + ax + \frac{a}{4}, & (x < 1) \\ a^x, & (x \geq 1) \end{cases}$, determine the range of values for the real number $a$ for which the function $y = f(x)$ is monotonically increasing on $(-\infty, +\infty)$.

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