
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
Consider the sequence $1, -4, 3, -8, 5, -12, \ldots$ whose $n$th term is $(-1)^{n+1} \cdot (2n - 1)$ if $n$ is odd and $(-1)^{n+1} \cdot 2n$ if $n$ is even. Calculate the average of the first $300$ terms of this sequence.
A) $-100$
B) $-76$
C) $-38$
D) $0$

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