
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
A parametric graph is defined by:
\[
x = \cos t + \frac{t}{3}, \quad y = \sin t.
\]
Determine the number of times the graph intersects itself between \(x = 3\) and \(x = 45\).

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