
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 parabola $y^2 = ax$ has its directrix as $x = -1$, and its focus is $F$.  
(1) Find the value of $a$;  
(2) A line passing through the point $F$ intersects the parabola at points $A(x_1, y_1)$ and $B(x_2, y_2)$. If $x_1 + x_2 = 6$, find the length of chord $AB$.

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