
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 $f(x)= \begin{cases}(\frac {1}{2})^{x}, & x\geqslant 0 \\ (\frac {1}{e})^{x}, & x < 0\end{cases}$, if for any $x\in[1-2a,1+2a]$, the inequality $f(2x+a)\geqslant [f(x)]^{3}$ always holds, determine the range of values for the real number $a$.

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