
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 $A$: $a_1, a_2, a_3, \ldots, a_n$ ($n \ge 3, n \in \mathbb{N}^*$), define $T_A = \{x | x=a_i \cdot a_j, 1 \leq i < j \leq n, i, j \in \mathbb{N}^*\}$. Let $\text{card}(T_A)$ represent the number of elements in the set $T_A$. (For instance, if $A: 1, 2, 4$, then $\text{card}(T_A) = 3$). If $\frac{a_{i+1}}{a_i} = c$ (where $c$ is a constant, and $|c| > 1$, for $1 \leq i \leq n-1$), then $\text{card}(T_A)$ equals ______.

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