
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 sequence $\{a_{n}\}$ where each term is non-zero, with the sum of the first $n$ terms denoted as $S_{n}$, $a_{1}=-1$, $4\leqslant a_{3}\leqslant 8$, $a_{2024} \lt 0$, and $2a_{n}a_{n+2}+a_{n+1}a_{n+3}=0$, find $a_{5}=$______; the maximum value of $S_{2024}$ is equal to ______.

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