
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 $A + B = \{x | x = x_1 + x_2, x_1 \in A, x_2 \in B\}$.  
If the largest element in the set $A + B$ is $2a + 1$, then the range of $a$ is ▲.

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