
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 a sequence $\{a\_n\}$, its first $n$ terms sum is $S\_n$. $a\_1= \frac {1}{5}$, and for any positive integers $m$, $n$, $a_{n+m}=a_{n}⋅a_{m}$. If $S_{n} < a$ holds for any $n∈N^*$, the minimum value of the real number $a$ is _____ .

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