
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 pentagon $FGHIJ$, $GH=HI=IJ=3$ units, $\angle J$ is right angle, $m\angle F = m\angle G = 90^\circ$, and $m\angle H = 135^\circ$. The length of segment $FJ$ can be expressed in simplest radical form as $c+3\sqrt{d}$ units. What is the value of $c+d$?

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