
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
Let the function $f(x)$ satisfy $f(x) = f\left(\frac{1}{{x+1}})$. The domain is $D=\left[0,+\infty \right)$, and the range is $A$. If the set $\{y|y=f(x), x\in \left[0,a\right]\}$ can take on all values in $A$, then the range of parameter $a$ is ____.

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