
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
The sequence ${a_n}$ satisfies $a_1=1$, $|a_n-a_{n-1}|=n^2$ ($n\in\mathbb{N}^*$ and $n\geq 2$). If the sequence ${a_{2n-1}}$ is increasing, the sequence ${a_{2n}}$ is decreasing, and $a_1>a_2$, then $a_{99}=\_\_\_\_\_\_.$

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