
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 $\{a_n\}$ be a decreasing geometric sequence, with $a_1+a_2=11$ and $a_1 \cdot a_2=10$, find the value of $\log a_1 + \log a_2 + \log a_3 + \ldots + \log a_{10}$.

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