
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
Let $\mathrm{A}=\left\{a_{1}, a_{2}, \cdots, a_{7}\right\}$, where $a_{i}$ are integers. Define $n_{A}$ as the number of ordered triples $(x, y, z)$ such that $x<y$, $x+y=z$, and $x, y, z \in A$. What is the maximum possible value of $n_{A}$?

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