
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 $a$, $b$, and $c$ are the lengths of the sides opposite to the angles $\angle A$, $\angle B$, and $\angle C$ respectively in $\triangle ABC$, and also that $\angle A = 60^\circ$, what is the value of $\frac{c}{a + b} + \frac{b}{a + c}$?

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