
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  $f(n)=1 \times 3 \times 5 \times \cdots \times (2n-1)$ . Compute the remainder when  $f(1)+f(2)+f(3)+\cdots +f(2016)$  is divided by  $100.$ *Proposed by James Lin*

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