
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 \( f(x) = \frac{x + a}{x^2 + \frac{1}{2}} \), where \( x \) is a real number and the maximum value of \( f(x) \) is \( \frac{1}{2} \) and the minimum value of \( f(x) \) is \( -1 \). If \( t = f(0) \), find the value of \( t \).

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