
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 \( g : \mathbb{R} \to \mathbb{R} \) be a function such that
\[
g((x + y)^2) = g(x)^2 + 2xy + y^2
\]
for all real numbers \( x \) and \( y \). Determine the number, \( m \), of possible values for \( g(1) \) and their sum, \( t \). Calculate \( m \times t \).

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