
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 that $\{a_n\}$ is an arithmetic sequence, and $S_n$ is the sum of its first $n$ terms, if $a_1 > 0$, $d < 0$, and $S_4 = S_8$, determine the largest natural number $n$ for which $S_n > 0$ holds.

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