
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 \( a_1, a_2, a_3, a_4 \) are 4 distinct numbers chosen from \( 1, 2, \cdots, 100 \), satisfying
$$
\left(a_1^2 + a_2^2 + a_3^2\right)\left(a_2^2 + a_3^2 + a_4^2\right) = \left(a_1 a_2 + a_2 a_3 + a_3 a_4\right)^2,
$$
determine the number of such ordered tuples \( (a_1, a_2, a_3, a_4) \).

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