
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 $f(x)=\begin{cases}\log_{a}x, & x > 0 \\ |x+3|, & -4\leqslant x < 0\end{cases} (a > 0\text{ and }a\neq 1),$ determine the range of $a$ if there are exactly two points on the graph of $f(x)$ that are symmetric about the $y$-axis.

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