biochemistry - Synthesis of tripeptide using Merrifield peptide synthesis procedure - Inclusion of asparagine

I am supposed to synthesize tripeptide, $\mathrm{Ala-Asn-Phe}$, using Merrifield peptide synthesis procedure. Accordingly, I have done followings:

1. Attached protected $\mathrm{Phe}$ as the first amino acid.


2. Got rid of protecting group ($\mathrm{BOC}$)


3. Added asparagine with 2 protecting groups - $\mathrm{BOC}$ for $\alpha$-$\ce{NH2}$ group and $\mathrm{FMOC}$ for the $\gamma$-$\ce{NH2}$ group.


4. Got rid of $\mathrm{BOC}$ and added $\mathrm{Ala}$ protected with $\mathrm{BOC}$.


5. Got rid of $\mathrm{BOC}$ and $\mathrm{FMOC}$, and used $\ce{HF}$ to release the peptide.

Is this going to work? The thing that worries me the most is the $\gamma$-amino group and using $\mathrm{FMOC}$ - is that a good idea?