
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
Divide 17 into two parts such that three-quarters of one part is larger by $a$ (where $a > 0$) than five-sixths of the other part. Within what boundaries can the value of $a$ vary to ensure the problem always remains solvable?

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