
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
Let the function \( f(x) = \sqrt{x^{2} + 1} - a x \), where \( a > 0 \).
1. Solve the inequality \( f(x) \leq 1 \).
2. Determine the range of values for \( a \) such that the function \( f(x) \) is monotonic on \( [0, +\infty) \).

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