
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 function $f(x) = x^2 + 2ax - 1$

(1) If $f(1) = 2$, find the value of the real number $a$, and find the minimum value of the function $f(x)$ at this time;  
(2) If $f(x)$ is an even function, find the value of the real number $a$;  
(3) If $f(x)$ is a decreasing function on $(-\infty, 4]$, then find the range of the real number $a$.

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