
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 \( A = \{ x \mid -1 \leqslant x \leqslant a \} \neq \varnothing \), \( B = \{ y \mid y = x + 1, x \in A \} \), and \( C = \{ y \mid y = x^2, x \in A \} \). If \( B = C \), find the value of the real number \( a \).

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