
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 $$f(x)= \sqrt {x^{2}+1}-ax$$, where $a>0$.  
(1) If $2f(1)=f(-1)$, find the value of $a$;  
(2) When $a\geq1$, determine the monotonicity of the function $f(x)$ on the interval $[0,+\infty)$;  
(3) If the function $f(x)$ is increasing on the interval $[1,+\infty)$, find the range of values for $a$.

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