
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 a sequence $\{a_n\}$ that satisfies $a_1 = t$, $a_{n+1} - a_n + 2 = 0$ ($t \in \mathbb{N}^*, n \in \mathbb{N}^*$), let the maximum value of the sum of the first n terms of the sequence $\{a_n\}$ be $f(t)$. Find the expression for $f(t)$.

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