
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
Let $H$ be a point on the extension of side $BC$ of parallelogram $ABCD$ such that $BH = 3BC$. $AH$ intersects diagonal $BD$ at point $I$ and side $AD$ at point $J$. If $JI = 30$ and $HI = 45$, find the length of $AJ$.

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