
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(t) = 2sin(t), where t belongs to the interval [π/6, π/2], for all real numbers m within the range of f(t), solve the inequality 2x^2 + mx - 2 < m + 2x.

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