
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 the arithmetic sequence {a<sub>n</sub>}, where the sum of the first n terms, S<sub>n</sub>, is represented by S<sub>n</sub>, if a<sub>7</sub>=5 and S<sub>5</sub>=-55, find the minimum value of nS<sub>n</sub>.

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