
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
Given an integer sequence \(\{a_{n}\}\) such that \(a_{3}=-1\) and \(a_{7}=4\), the first 6 terms form an arithmetic sequence, and starting from the 5th term, it forms a geometric sequence. Find the positive integer \(m\) such that \(a_{m} + a_{m+1} + a_{m+2} = a_{m} a_{m+1} a_{m+2}\). What is \(m\)?

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