
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 that four integers \( a, b, c, d \) are all even numbers, and \( 0 < a < b < c < d \), with \( d - a = 90 \). If \( a, b, c \) form an arithmetic sequence and \( b, c, d \) form a geometric sequence, then find the value of \( a + b + c + d \).

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