
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

Provide short calculations for the following questions:

a) What is the value of the fraction

$$
\frac{423134 \cdot 846267 - 423133}{423133 \cdot 846267 + 423134}?
$$

b) What number must be subtracted from the numerator of the fraction $\frac{52367}{47633}$ and added to its denominator to simplify the fraction to $\frac{17}{83}$?

c) What is the sum of the following fractions?

$$
\frac{7}{2 \cdot 9}+\frac{7}{9 \cdot 16}+\frac{7}{16 \cdot 23}+\cdots+\frac{7}{65 \cdot 72}
$$

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