
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 the solution to the equation x^3 + x - 4 = 0 lies within the interval (k, k + $\frac{1}{2}$), where k is an integer multiple of $\frac{1}{2}$, determine the value of the real number k.

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