
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 the function $f(x)=\begin{cases} (-1)^{n}\sin \frac{πx}{2}+2n,&x\in[2n,2n+1) \\ (-1)^{n+1}\sin \frac{πx}{2}+2n+2,&x\in[2n+1,2n+2) \end{cases}$, where $n\in N$, and the sequence ${a_{m}}$ satisfies $a_{m}=f(m)$ $(m\in N^{*})$. Let $S_{m}$ be the sum of the first $m$ terms of the sequence ${a_{m}}$. Determine the value of $S_{105}-S_{96}$.

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