
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 positive geometric sequence $\{a_n\}$, where $a_5a_{2n-5}=10^{2n}$ $(n\geqslant 3,n\in N^{*})$, find the value of the expression $\lg a_1+\lg a_2+\lg a_3+\ldots+\lg a_n$ when $n\geqslant 1$, $n\in N^{*}$.

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