
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 the sum of the first $n$ terms ($S_n$) of an arithmetic sequence ${{a_n}}$ satisfies ${S_5} < {S_6}$ and ${S_6}={S_7} > {S_8}$, the correct conclusion is:
\[
\begin{array}{*{20}{c}}
{(1)}{S_6}\text{ and }{S_7}\text{ are both the maximum values of }{S_n}\\
{(2)}{a_7}=0\\
{(3)}\text{ The common difference }d < 0\\
{(4)}{S_9} > {S_5}
\end{array}
\]

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