
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) = 3x - 2, find the minimum value of the real number λ such that there exists a $θ ∈ (0, \frac{π}{2}]$ that satisfies the inequality $f(cos^{2}θ + λsinθ - 1) + \frac{1}{2} ≥ 0$.

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