
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
The precent ages in years of two brothers  $A$  and  $B$ ,and their father  $C$  are three distinct positive integers  $a ,b$  and  $c$  respectively .Suppose  $\frac{b-1}{a-1}$  and  $\frac{b+1}{a+1}$  are two consecutive integers , and   $\frac{c-1}{b-1}$  and  $\frac{c+1}{b+1}$   are two consecutive integers . If  $a+b+c\le 150$  , determine  $a,b$  and  $c$ .

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