
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
In triangle $ABC$, let the sides opposite to angles $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively. Given that $\cos A = -\frac{\sqrt{10}}{10}$, $b = \sqrt{2}$, and $c = \sqrt{5}$:  
(1) Find the value of $a$;  
(2) Calculate the value of $\cos(B - A)$.

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