
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
Let $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, for example, $\lfloor 2.9 \rfloor = 2$, $\lfloor -4.1 \rfloor = -5$. Given $f(x)= \begin{cases} 2^{x}, & \text{if } x < 1,\\ x-\lfloor x \rfloor, & \text{if } x \geqslant 1, \end{cases}$ then $f(f( \frac {5}{2}))=$ \_\_\_\_\_\_.

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