
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 \( A = \{a_1, a_2, \cdots, a_7\} \). Here \( a_i \in \mathbf{Z}' \). Let \( n_A \) represent the number of 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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