
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 $\sin\alpha + \cos\alpha = \frac{1}{5}$. Find:  
(1) $\sin\alpha - \cos\alpha$;  
(2) $\sin^3\alpha + \cos^3\alpha$.  
(Reference formula: $a^3 + b^3 = (a - b)(a^2 - ab + b^2)$)

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