
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 $a\_1, a\_2, ..., a\_n$ be a sequence of positive terms, and let $T\_n$ be the product of the first $n$ terms. Define the "relative cumulative product" as $\lg (T\_1 \cdot T\_2 \cdot ...T\_n)$. If a sequence of 2013 positive terms $a\_1, a\_2, ..., a\_2013$ has a "relative cumulative product" of 2013, then the "relative cumulative product" of the sequence $10, a\_1, a\_2, ..., a\_2013$ with 2014 terms is $\boxed{\ }$.

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