
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
In a certain project, the number of days required by team A working alone is \( a \) times the number of days required by teams B and C working together; the number of days required by team B working alone is \( b \) times the number of days required by teams A and C working together; and the number of days required by team C working alone is \( c \) times the number of days required by teams A and B working together. Find the value of 

\[
\frac{1}{a+1} + \frac{1}{b+1} + \frac{1}{c+1}
\]

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