
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 $f(x)= \begin{cases} x^{2}+(4a-3)x+3a, & x < 0 \\ \log _{a}(x+1)+1, & x\geqslant 0 \end{cases}$, where $(a > 0$ and $a\neq 1)$, the function is monotonically decreasing on $\mathbb{R}$.
(1) The range of $a$ is $\_\_\_\_\_\_$;
(2) If the equation $|f(x)|=2-x$ has exactly two distinct real solutions in terms of $x$, then the range of $a$ is $\_\_\_\_\_\_$.

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