
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
Let $a < b < c$ be three integers such that $a, b, c$ is an arithmetic progression and $c, a, b$ is a geometric progression. Further assume that $a, b, c$ are multiples of 5. What is the smallest possible value of $c$ where all numbers are positive?

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