
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
A $\frac 1q$ -array is constructed in a similar manner to a $\frac 1p$ -array, but the first entry of each row after the first is obtained by multiplying the first entry of the previous row by $\frac{1}{3q}$ instead of $\frac{1}{2q}$. Each succeeding term in a row continues to be $\frac 1q$ times the previous term. Compute the total sum of all terms in a $\frac{1}{1004}$ -array.

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