
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 \(\mathrm{f}(\mathrm{x}) = \mathrm{x} - \ln(\mathrm{ax} + 2 \mathrm{a} + 1) + 2\), if \(\mathrm{f}(\mathrm{x}) \geq 0\) holds for any \(\mathrm{x} \geq -2\), find the range of the real number \(\mathrm{a}\).

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