
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 "number array" as shown on the left, where each column forms an arithmetic sequence, and starting from the third row, each row forms a geometric sequence with a common ratio equal to that of every other row. The first column is $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, ..., the second column is $\frac{1}{4}$, $\frac{1}{4}$, $\frac{3}{8}$, ..., and the third column is $\frac{1}{4}$, $\frac{1}{4}$, $\frac{3}{16}$, ... . Denote the element in the $i$-th row and $j$-th column as ${a_{ij}}\left( {i \geqslant j,i,j \in {N^ * }} \right)$, find the value of ${a_{83}}$.

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