How to configure NAT on cisco in this situation?

Question

System administration

Friends, the second day I suffer. There is the following configuration:

Where R1:

interface FastEthernet0/0
 ip address 172.16.0.1 255.255.255.252
 duplex auto
 speed auto
!
interface FastEthernet0/1
 ip address 10.1.1.1 255.255.255.0
 duplex auto
 speed auto
!
interface Vlan1
 no ip address
 shutdown
!
router ospf 1
 log-adjacency-changes
 network 172.16.0.0 0.0.0.3 area 1

R_NAT:

interface FastEthernet0/0
 ip address 172.16.0.2 255.255.255.252
 ip nat inside
 duplex auto
 speed auto
!
interface FastEthernet0/1
 ip address 8.8.8.1 255.255.255.0
 ip nat outside
 duplex auto
 speed auto
!
interface Vlan1
 no ip address
 shutdown
!
router ospf 1
 log-adjacency-changes
 network 172.16.0.0 0.0.0.3 area 1
 network 8.8.8.0 0.0.0.255 area 1
!
ip nat pool NAT_POOL 8.8.8.1 8.8.8.1 netmask 255.255.255.0
ip nat inside source list 1 pool NAT_POOL overload
ip classless
!
ip flow-export version 9
!
!
access-list 1 permit 10.1.1.0 0.0.0.255

With this configuration, NAT works, as indicated show ip nat translationsby , but the ping coming from 10.1.1.2 goes through R_NAT (where the substitution occurs), reaches 8.8.8.8, returns to R_NAT (where the reverse substitution occurs) and is discarded. Because there is no route to the 10.1.1.0/24 network on R_NAT. If you add a route, then everything starts working, but 8.8.8.8 starts to ping the 10.1.1.0/24 network, and this should not be!
Tell me how to fix this?
PS: Routing can only be used by OSPF.