
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 that functions $f(x)$ and $g(x)$ are defined on the set of real numbers, where $f(x)$ is an odd function and $g(x)$ is an even function. Additionally, $f(x) + g(x) = x^2 + ax + 2a - 1$ (where $a$ is a constant), and $f(1) = 2$. Determine the expression for $g(t)$.

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