
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 \( a > 0 \), and the function \( f(x) = x - a \sqrt{x^{2} + 1} + a \).

(1) If \( f(x) \) is an increasing function on the interval \( (0, 1] \), find the range of values for \( a \).

(2) Find the maximum value of \( f(x) \) on the interval \( (0, 1] \).

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