
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 $f(x)=ax-|x+1| (x\in R)$.
(1) Let function $g(x)$ be an odd function defined on $R$, and when $x > 0$, $g(x)=f(x)$, find the analytical expression of $g(x)$;
(2) If function $f(x)$ has a maximum value, find the range of real number $a$.

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