
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
a,b,c are positives  with  21ab+2bc+8ca \leq 12 . Find the least  possoble  value  of the  expresion 1/a + 2/b + 3/c.
Thanks

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