
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 $f(x) = \frac{2x^{2}}{x+1}$, and $g(x) = ax + 5 - 2a$ with $a > 0$, find the range of values for $a$ such that for every $x_1 \in [0, 1]$, there always exists $x_0 \in [0, 1]$ such that $g(x_0) = f(x_1)$.

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