
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 the function $f(x)= \begin{cases} x\ln x, & x\geqslant 1\\ \frac {\ln x}{x}, & 0 < x < 1\end{cases}$. If $\{a_n\}$ is a geometric sequence with a common ratio greater than $0$, and $a_3a_4a_5=1$, and $f(a_1)+f(a_2)+\ldots+f(a_6)=2a_1$, then $a_1=$ ______.

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