
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
Proposition p: The function $f(x) = \begin{cases} x^{2}+(4a-3)x+3a, & x<0 \\ \log_{a}(x+1)+1, & x\geq0\end{cases}$ ($a>0$, and $a\neq1$) is a monotonically decreasing function on $\mathbb{R}$, Proposition q: $\forall x\in[0, \frac{\sqrt{2}}{2}], x^2-a\leq0$ always holds.  
(1) Find the range of values for $a$ when proposition q is true;  
(2) If proposition $p\land q$ is false, and $p\lor q$ is true, find the range of values for $a$.

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