
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 two vectors in the plane, **a** = (1, 2sinθ) and **b** = (5cosθ, 3).  
(1) If **a** is parallel to **b**, find the value of sin2θ;  
(2) If **a** is perpendicular to **b**, find the value of tan(θ＋).

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