
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 function $f(x)$ with domain $\mathbb{R}$ that satisfies $f(x) + f(x+2) = 2x^2 + 3$, and $f(x+1) - f(x-1) = 2x - 1$. If $f(t-1)$, $1$, and $f(t)$ form an arithmetic sequence, then the value of $t$ is.

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