
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
An odd function $f(x)$ is defined on $\mathbb{R}$, and for $x > 0$, the function is expressed as $$f(x) = \frac {2}{x} - 1$$  
(1) Determine the expression for the function when $x < 0$.  
(2) Write the expression for the function $f(x)$ on $\mathbb{R}$ in piecewise form. Calculate the value of $a$ when $f(a) = 3$.

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