
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 a differentiable function $f(x)$, determine the value of 
$$\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{3\Delta x}.$$
A) $f'(1)$  
B) $3f'(1)$  
C) $\frac{1}{3}f'(1)$  
D) $f'(3)$

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