
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 $$f(x)= \begin{cases} \left.\begin{matrix}x^{3} & (x＞1) \\ -x^{2}+2x & (x≤1).\end{matrix}\right.\end{cases}$$, determine the possible values of $a$ such that $f(a)=- \frac {5}{4}$.

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