
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
If all terms of the geometric sequence $\left\{ a_n \right\}$ are positive, and $a_4a_9+a_5a_8+a_6a_7=300$, then $\lg a_1+\lg a_2+\cdots+\cdots+\lg a_{12}=$ __________.

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