
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 that the function $y = f(x)$ is a periodic function defined on $\mathbb{R}$ with period $T = 5$. The function $y = f(x)$ for $-1 \leq x \leq 1$ is an odd function, and it is a quadratic function on the interval $[1, 4]$. The function takes its minimum value of $-5$ at $x = 2$. Determine:
(1) The value of $f(1) + f(4)$;
(2) The explicit expression of $y = f(x)$ for $x \in [1, 4]$.

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