
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 sets $A=\{0, 1\}, B=\{a^2, 2a\}$, where $a\in\mathbb{R}$, we define the set $\{x | x = x_1 + x_2, x_1 \in A, x_2 \in B\}$ as $A+B$. If the largest element in the set $A+B$ is $2a+1$, find the range of values for $a$.

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