
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 increasing sequence of 8 real numbers, Diana listed all possible sequences of 4 consecutive numbers. It turned out that two of the five new sequences are arithmetic progressions with common differences of 4 and 36, respectively, and one of the sequences is a geometric progression. Find the largest of the given 8 numbers. Mention all possible options.

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