
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 minimum value of the function f(x) = x - ln(x + a) is 0, where a > 0.

1. Find the value of a.
2. If for any x ∈ [0, +∞), there is f(x) ≤ kx², find the minimum value of the real number k.

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