
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
Select three elements from the set $A=\{1,2,3,4,5\}$ to form an ordered triple $(a_1, a_2, a_3)$, with the condition that $a_1 < a_2 < a_3$.
(Ⅰ) From all possible ordered triples, find the probability that the sum of its elements is equal to 10.
(Ⅱ) Define the "term index distance" for an ordered triple $(a_1, a_2, a_3)$ as $d = |a_1 - 1| + |a_2 - 2| + |a_3 - 3|$. From all possible ordered triples, find the probability that the "term index distance" $d$ is an even number.

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