
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 $f(x)=\frac{x}{ax+b}$, where $a$ and $b$ are constants and $a\neq 0$, it is known that $f(4)=\frac{4}{3}$. The equation $f(x)=x$ has a unique solution. Find the analytical expression of the function $f(x)$ and the value of $f[f(-3)]$.

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