
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 the power function $f(x) = (m^2 - 5m + 7)x^{-m-1}$ ($m \in \mathbb{R}$) is an even function.  
(1) Find the value of $f\left( \frac{1}{2} \right)$.  
(2) If $f(2a+1) = f(a)$, find the value of the real number $a$.

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