
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 an even function $f(x)$ which is differentiable for all real values, and $f'(1)=1$. It is also given that $f(x+2)=f(x-2)$. Find the slope of the tangent to the curve $y=f(x)$ at $x=-5$.

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