
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 $5 \times 5$ digital square matrix $\left[ \begin{matrix} & {{a}_{11}} & {{a}_{12}} & {{a}_{13}} & {{a}_{14}} & {{a}_{15}} \\ & {{a}_{21}} & {{a}_{22}} & {{a}_{23}} & {{a}_{24}} & {{a}_{25}} \\ & {{a}_{31}} & {{a}_{32}} & {{a}_{33}} & {{a}_{34}} & {{a}_{35}} \\ & {{a}_{41}} & {{a}_{42}} & {{a}_{43}} & {{a}_{44}} & {{a}_{45}} \\ & {{a}_{51}} & {{a}_{52}} & {{a}_{53}} & {{a}_{54}} & {{a}_{55}} \\ \end{matrix} \right]$, where ${{a}_{ij}}= \begin{cases} 1, j \text{ is a multiple of } i \\ -1, j \text{ is not a multiple of } i \end{cases}$, find the value of $\sum\limits_{j=2}^{5}{{{a}_{3j}}}+\sum\limits_{i=2}^{4}{{{a}_{i4}}}$

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