
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
To any triangle with side lengths  $a,b,c$  and the corresponding angles  $\alpha, \beta, \gamma$  (measured in radians), the 6-tuple  $(a,b,c,\alpha, \beta, \gamma)$  is assigned. Find the minimum possible number  $n$  of distinct terms in the 6-tuple assigned to a scalene triangle.


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