
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 four unequal, positive integers \(a, b, c,\) and \(N\) where \(N=5a+3b+5c\), \(N=4a+5b+4c\), and \(N\) is between 131 and 150, calculate the value of \(a+b+c\).

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