
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 book is published in three volumes, the pages being numbered from  $1$  onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is  $50$  more than that in the first volume, and the number pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is  $1709$ . If  $n$  is the last page number, what is the largest prime factor of  $n$ ?

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