
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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Suppose there exists a real number $a$ such that the function $f(x) = \begin{cases} -x^{2}+2(a+1)x+4 & 0 < x \leqslant 1 \\ x^{a} & x > 1 \end{cases}$ is a decreasing function on $(0,+\infty)$, find the range of values for the real number $a$.

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