
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 + 2cos(x) + λ, for any three numbers x₁, x₂, x₃ in the interval [0, π/2], determine the range of λ such that there exists a triangle with side lengths f(x₁), f(x₂), and f(x₃).

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