
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
(1) Given that the function $f(x)$ is an odd function defined on $\mathbb{R}$, and $f(x) = 2^{-x} + x^2$ when $x \in (-\infty, 0)$, find the value of $f(2)$.

(2) Find the value of $\sin x$ when the function $f(x) = 3\sin x + 6\cos x$ reaches its maximum value.

(3) A trirectangular tetrahedron $A-BCD$ has three mutually perpendicular edges $AB$, $BC$, and $CD$ with lengths $3$, $2$, and $1$, respectively. All vertices $A$, $B$, $C$, and $D$ lie on the surface of sphere $O$. Find the surface area of sphere $O$.

(4) In an obtuse triangle $\triangle ABC$, the lengths of sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ are $4$, $3$, and $c$ respectively. Find the range of values for $c$.

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