
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 $f(x)= \begin{cases} f(x+1), & -2 < x < 0 \\ 2x+1, & 0\leqslant x < 2 \\ x^{2}-1, & x\geqslant 2\end{cases}$;  
$(1)$ Find the value of $f(- \dfrac {3}{2})$;  
$(2)$ If $f(a)=4$ and $a > 0$, find the value of the real number $a$.

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