
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 $f(x) = \begin{cases} x\ln x & ,x\geq 1 \\ \frac {\ln x}{x} & ,0<x<1 \end{cases}$, if $\{a_n\}$ is a geometric sequence with a common ratio greater than 0, and $a_3a_4a_5=1$, if $f(a_1)+f(a_2)+\ldots+f(a_6)=2a_1$, then $a_1= \boxed{\text{\_\_\_\_\_\_}}$.

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