
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 the function \( f(x) = x^2 + x + m \) where \( m \in \mathbf{R}^{+} \), if \( f(t) < 0 \), determine the existence of zeros of the function \( y = f(x) \) in the interval \( (t, t+1) \).

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